79 lines
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3.7 KiB
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79 lines
No EOL
3.7 KiB
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\addtocounter{customchapter}{1}
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\chapter{Conclusions and future work}
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\label{chap:conclusions-and-future-work}
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\section{Conclusion}
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\label{sec:conclusion}
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\subsection{State of work at the end of the internship}
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At the end of this internship we now have:
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\begin{itemize}
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\item A model capable to find structure in collections of bipartite network.
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Enabling the possibility to bring together networks that may have not
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seem evident to put together.
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\item A clustering method that is able to partition a collection into
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collections that are similar in their structures.
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\item All the described methods implemented into an \texttt{R} package.
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\end{itemize}
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\subsection{Difficulties encountered}
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\label{ssec:difficulties-encountered}
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\paragraph{Local optima} While using our clustering on data
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from~\cite{doreRelativeEffectsAnthropogenic2021} we obtained quite interesting
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results but investigating further, we noticed that the clustering on such big
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collections ($M=123$) was not fully reproducible. It depends a lot on the random
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generator seed and as there is no possibility to merge back
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collections
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the clustering dendrograms do not stabilize on large collections.
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This, currently, prevents us to clusterize large collections.
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We suspect that our model selection method gets stuck on local optima
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of the BIC-L.
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\paragraph{Large penalties with free mixture models}
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We observed while testing clustering with the different models that
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the $\pi$, $\rho$ and $\pi\rho$ model, with their increased number of parameters
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for block memberships parameters tends to give smaller BIC-L criterion values
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while having a higher Evidence Lower Bound than the \emph{iid}.
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This arises because of the penalties on the block memberships and supports that
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increase significantly and exceeds the gain on the ELBO and the diminution of
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the connectivity parameters.
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\section{Future work}
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\label{sec:future-work}
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\paragraph{Fixing local optima}
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We are currently investigating the procedure and code to see if reducing or
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escaping seed dependance is possible and would allow escaping the local optima.
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\paragraph{Identifiability}
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As stated in section~\ref{sec:model-identifiability}, we only have
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identifiability for the \emph{iid}-colBiSBM and we will work on establishing
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identifiability for $\pi$, $\rho$ and $\pi\rho$ models which are the most
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challenging with regard to identifiability.
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\paragraph{Finding a trade-off between \emph{iid} and $\pi\rho$}
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An idea to tackle the problem of large penalties with $\pi$, $\rho$ and
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$\pi\rho$ could be to suppose that the block memberships
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for network $m$ are themselves the realizations of random variables and
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thus introduce sort of a mixed effect model. This may allow a self-penalization
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that could keep the flexibility intended in these models.
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\paragraph{More ecological applications} We have leads to apply the models on
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interesting cases, among them are the following:
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\begin{itemize}
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\item Networks that are spaced along an altitude gradient, which could be
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accounted for in the dissimilarity measure for instance.
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\item Collection of different sorts of interactions (plants-seed dispersors,
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host-parasites, \dots)
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\end{itemize}
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\paragraph{Turning this work into an article} We will work in the upcoming
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months to write an article about the method.
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\paragraph{Comparison to other graphs clustering methods}
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Recent work have been comparing
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\texttt{colSBM}~\parencite{chabert-liddellLearningCommonStructures2024a} and
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\texttt{graphclust}~\parencite{rebafkaModelbasedClusteringMultiple2023} assessing various
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capabilities of the models and particularly focusing on networks clustering.
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We will reproduce and adapt the analysis to test other simulation settings that
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were not considered in this work. |